CRYSTAL GEOMETRY. An Introduction to the theory of lattice transformation in metallic materials with Matlab applications. 8 courses of 2 hours

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Transcription:

CRYSTAL GEOMETRY An Introduction to the theory of lattice transformation in metallic materials with Matlab applications Français Cours 0 : lundi 4 décembre 9h30-11h30 Cours 1 : vendredi 8 décembre 9h30-11h30 Cours 2 : lundi 11 décembre 9h30-11h30 Cours 3 : vendredi 15 décembre 9h30-11h30 Cours 4 : lundi 8 janvier 2018 9h30-11h30 Cours 5 : mercredi 10 décembre 9h30-11h30 Cours 6 : lundi 15 janvier 9h30-11h30 Cours 7 : vendredi 19 janvier 9h30-11h30 8 courses of 2 hours English course 0: Monday 11 December 13h30-15h30 course 1: Friday 15 December 13h30-15h30 course 2: Monday 18 December 13h30-15h30 course 3: Monday 8th January 2018 13h30-15h30 course 4: Friday 12 January 13h30-15h30 course 5: Monday 15 January 13h30-15h30 course 6: Friday 19 January 13h30-15h30 course 7 : Monday 22 January 13h30-15h30 Jean-Sébastien LECOMTE ROOM DN1-005 LEM3

Part 0: Matlab & Matrix Algebra What is MATLAB? MATLAB Screen Variables, array, matrix, indexing Operators (Arithmetic, relational, logical) MATLAB Input and Output Display Facilities Flow Control Using of M-File Writing User Defined Functions Applied Exercise Symbolic Math Toolbox Matrix Algebra The use of the Matrix in crystallography Particular form of the square matrix Matrix algebra HomeWork n 1 Course 0 (en français) Lundi 4 décembre 9h30-11h30 (in English) Monday 11 December 13h30-15h30 Part I: Elements of crystallography 1.1 Crystal system (crystal family) 1.2 Reciprocal lattice 1.3 The metric tensor of a crystal 1.4 BCC and FCC in a primitive unit cell 1.5 Correspondence 1.6 The crystalline directions 1.7 Crystal planes 1.8 The indexing of hexagonal lattices HomeWork n 2 Cours 1 : vendredi 8 décembre 9h30-11h30 course 1: Friday 15 December 13h30-15h30

Part II: Change of basis 2.1 Vector equation 2.2 Establishment of the matrix of the change of base 2.3 Epitaxy 2.4 Available orientation descriptors 2.4.1 Rotation Matrix 2.4.2 Euler Angles 2.4.3 Miller Indices 2.4.4 Axis/Angle of Rotation 2.4.5 Rodrigues Vector 2.4.6 Quaternion 2.5 Symmetry operations 2.5.1 Inversion center (Z) 2.5.2 The axis of symmetry (X) (proper axis) 2.5.3 Symmetry Plane (Σ) 2.5.4 Rotary inversions (Δ) ou rotoinversion (improper axes) 2.6 The rigid body rotation 2.7 Pole Figure 2.7.1 stereographic projection 2.7.2 equal-area projection 2.8 Inverse Pole Figure HomeWork n 3 Cours 2 : lundi 11 décembre 9h30-11h30 course 2: Monday 18 December 13h30-15h30

Part II BIS: Introduction to MTEX 2.9 Orientation Mapping 2.10 Orientation Distribution 2.11 Orientation Spread 2.12 Misorientation Distribution 2.12.1 Mackenzie Distribution 2.13 Misorientations, Disorientations 2.14 Mean Orientation 2.15 Orientation Spread Anisotropy 2.16 KAM & GOS HomeWork n 4 Cours 3 : vendredi 15 décembre 9h30-11h30 course 3: Monday 8th January 2018 13h30-15h30 Part IV: Orientation relationship and orientation variants 3.1 Twinning 3.1.1 Twinning in FCC 3.1.2 Twinning in BCC 3.1.3 Twinning in HCP 3.2 Orientation relationship between FCC and HCP 3.3 Orientation relationship between HCP and BCC 3.4 Orientation Relationship between FCC and BCC 3.4.1 Bain Orientation Relationship 3.4.2 Kurdjumov-Sachs Relationship 3.4.3 Nishiyama Orientation Relationship HomeWork n 5 Cours 4 : lundi 8 janvier 9h30-11h30 course 4: Friday 12 January 13h30-15h30

Part IV: Homogeneous lattice deformation 4.1 Homogeneous deformation 4.1.1 Unit matrix 4.1.2 Rotation Matrix 4.1.3 Pure deformation 4.1.4 Pure shear 4.1.5 Invariant deformation plane Strain ellipsoid and determination of principal diagonals 4.2 Special elements of crystallography 4.3 Relationships between the different deformation matrices HomeWork n 6 Cours 5 : mercredi 10 décembre 9h30-11h30 course 5: Monday 15 January 13h30-15h30 Part V: Shear in metal crystals 5.1 Schmid factor 5.2 Formation of mechanical twins 5.2.1 Twinning formation in BCC lattice 5.2.2 Twinning Formation in FCC lattice 5.2.3 Comparison between the BCC lattice and the FCC lattice 5.2.4 Twinning Formation in HCP lattice 5.3 Formation of martensite 5.3.1 γ ε Martensitic transformation 5.3.2 ε α Martensitic transformation 5.4 γ α Martensitic transformation 5.4.1 Kurdjumov and Sachs Model 5.4.2 Nishiyama Model 5.4.3 Bogers and Burgers Model 5.4.4 Pitsch Model HomeWork n 7 Cours 6 : lundi 15 janvier 9h30-11h30 course 6: Friday 19 January 13h30-15h30

Part VI: Crystallographic and phenomenological theory of martensitic transformation 6.1 Domain of validity 6.2 Basis of the crystallographic theory of phenomenological martensitic transformation 6.3 Wechsler, Lieberman and Read Theory 6.4 Bowles and Mackenzie Theory 6.5 Ross and Crocker Theory HomeWork n 8 Cours 7 : vendredi 19 décembre 9h30-11h30 course 7 : Monday 22 January 13h30-15h30

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